In most themes Colored Block functionality is exactly like the text block, but there is also an option to choose a block color, as well as add a block link, so that the whole block could lead to any URL you need:

In some themes Colored Block Shortcode lets you set a custom color at your choice using a color picker, rather than pick one of the pre-defined ones. Link settings may also differ.

Please see what kind of functionality for this shortcode is offered in your theme: